1. Jets, high-p T hadrons and prompt photons QM2011 student lecture 22 May 2011 Marco van Leeuwen, Utrecht University

2. 2 Hard processes in QCD Hard process: scale Q >>  QCD Hard scattering High-p T parton(photon) Q~p T Heavy flavour production m >>  QCD Cross section calculation can be split into Hard part: perturbative matrix element Soft part: parton density (PDF), fragmentation (FF) Soft parts, PDF, FF are universal: independent of hard process QM interference between hard and soft suppressed (by Q 2 /  2 ‘Higher Twist’) Factorization parton densitymatrix elementFF

3. 3 Seeing quarks and gluons In high-energy collisions, observe traces of quarks, gluons (‘jets’)

4. 4 Fragmentation and parton showers large Q 2 Q ~ m H ~  QCD FF Analytical calculations: Fragmentation Function D(z,  ) z=p h /E jet Only longitudinal dynamics High-energy parton (from hard scattering) Hadrons MC event generators implement ‘parton showers’ Longitudinal and transverse dynamics

5. 5 Jet Quenching 1)How is does the medium modify parton fragmentation? Energy-loss: reduced energy of leading hadron – enhancement of yield at low p T ? Broadening of shower? Path-length dependence Quark-gluon differences Final stage of fragmentation outside medium? 2)What does this tell us about the medium ? Density Nature of scattering centers? (elastic vs radiative; mass of scatt. centers) Time-evolution? High-energy parton (from hard scattering) Hadrons

6. 6 Medium-induced radition If <  f, multiple scatterings add coherently Zapp, QM09 L c =  f,max propagating parton radiated gluon Landau-Pomeranchuk-Migdal effect Formation time important Radiation sees length ~  f at once Energy loss depends on density: and nature of scattering centers (scattering cross section) Transport coefficient

7. 7 Testing volume (N coll ) scaling in Au+Au PHENIX Direct  spectra Scaled by N coll PHENIX, PRL 94, 232301 Direct  in A+A scales with N coll Centrality A+A initial state is incoherent superposition of p+p for hard probes

8. 8  0 R AA – high-p T suppression Hard partons lose energy in the hot matter  : no interactions Hadrons: energy loss R AA = 1 R AA < 1  0 : R AA ≈ 0.2  : R AA = 1

9. 9 Two extreme scenarios p+p Au+Au pTpT 1/N bin d 2 N/d 2 p T Scenario I P(  E) =  (  E 0 ) ‘Energy loss’ Shifts spectrum to left Scenario II P(  E) = a  (0) + b  (E) ‘Absorption’ Downward shift (or how P(  E) says it all) P(  E) encodes the full energy loss process R AA not sensitive to energy loss distribution, details of mechanism

10. 10 Four theory approaches Multiple-soft scattering (ASW-BDMPS) –Full interference (vacuum-medium + LPM) –Approximate scattering potential Opacity expansion (GLV/WHDG) –Interference terms order-by-order (first order default) –Dipole scattering potential 1/q 4 Higher Twist –Like GLV, but with fragmentation function evolution Hard Thermal Loop (AMY) –Most realistic medium –LPM interference fully treated –No finite-length effects (no L 2 dependence)

11. 11 Energy loss spectrum Brick L = 2 fm,  E/E = 0.2 E = 10 GeV Typical examples with fixed L  E/E> = 0.2 R 8 ~ R AA = 0.2 Significant probability to lose no energy (P(0)) Broad distribution, large E-loss (several GeV, up to  E/E = 1) Theory expectation: mix of partial transmission+continuous energy loss – Can we see this in experiment?

12. 12 Geometry Density profile Profile at  ~  form known Density along parton path Longitudinal expansion dilutes medium  Important effect Space-time evolution is taken into account in modeling

13. 13 Determining Bass et al, PRC79, 024901 ASW: HT: AMY: Large density: AMY: T ~ 400 MeV Transverse kick: qL ~ 10-20 GeV All formalisms can match R AA, but large differences in medium density At RHIC:  E large compared to E, differential measurements difficult After long discussions, it turns out that these differences are mostly due to uncontrolled approximations in the calculations  Best guess: the truth is somewhere in-between

14. 14 R AA at LHC ALICE PHENIX R AA at LHC: increase with p T  first sign of sensitivity to P(  E) ALICE, PLB 696, 30 Larger ‘dynamic range’ at LHC very important – stay tuned

15. 15 R AA RHIC and LHC II Overlaying the two results: PHENIX  0 and ALICE h ± p T -dependence not too different… N.B.: Large uncertainties in RHIC result at high p T

16. 16 Path length dependence: R AA vs L PHENIX, PRC 76, 034904 In Plane Out of Plane 3<p T <5 GeV/c R AA as function of angle with reaction plane Suppression depends on angle, path length Relation between RAA(  ) and v 2 :

17. 17 Path length dependence and v 2 PHENIX PRL105, 142301 v 2 at high p T due to energy loss Most calculations give too small effect Path length dependence stronger than expected? Depends strongly on geometry – stay tuned

18. 18 Di­hadron correlations associated  trigger 8 < p T trig < 15 GeV p T assoc > 3 GeV Use di-hadron correlations to probe the jet-structure in p+p, d+Au Near side Away side and Au+Au Combinatorial background

19. 19 p T assoc > 3 GeV p T assoc > 6 GeV d+Au Au+Au 20-40% Au+Au 0-5% Suppression of away-side yield in Au+Au collisions: energy loss High-p T hadron production in Au+Au dominated by (di-)jet fragmentation Di-hadrons at high-p T : recoil suppression

20. 20 Di­hadron yield suppression Away-side: Suppressed by factor 4-5  large energy loss Near side Away side STAR PRL 95, 152301 8 < p T,trig < 15 GeV Yield of additional particles in the jet Yield in balancing jet, after energy loss Near side: No modification  Fragmentation outside medium? Near side associated trigger Away side associated trigger

21. 21 Path length II: ‘surface bias’ Near side trigger, biases to small E-loss Away-side large L Away-side suppression I AA samples longer path-lengths than inclusives R AA

22. 22 L scaling: elastic vs radiative T. Renk, PRC76, 064905 R AA : input to fix density Radiative scenario fits data; elastic scenarios underestimate suppression Indirect measure of path-length dependence: single hadrons and di-hadrons probe different path length distributions Confirms L 2 dependence  radiative loss dominates

23. 23 Intermediate p T Enhanced baryon/meson ratio –Hadronisation by coalescence? Enhanced near-side yield at large  ‘ridge’ –Triangular flow? Away-side double-peak structure –Mach cone? –Triangular flow? So far, focused on high-p T Where factorisation may hold p T > 1-4 GeV Some other ‘puzzling’ (i.e. not dominated by jet fragmention+energy loss) observations at intermediate p T :

24. 24 Baryon excess STAR Preliminary B. Mohanty (STAR), QM08 High p T : Au+Au similar to p+p  Fragmentation dominates Baryon/meson = 0.2-0.5 Intermediate p T, 2 – 6 GeV Large baryon/meson ration in Au+Au

25. 25 Hadronisation through coalescence fragmenting parton: p h = z p, z<1 recombining partons: p 1 +p 2 =p h Fries, Muller et al Hwa, Yang et al Meson p T =2p T,parton Recombination of thermal (‘bulk’) partons produces baryons at larger p T Recombination enhances baryon/meson ratio Hot matter Baryon p T =3p T,parton R. Belmont, QM09 Note also: v 2 scaling

26. 26 Near-side Ridge 3 < p t,trig < 4 GeV/c Au+Au 0-10% STAR preliminary associated  trigger `Ridge’: associated yield at large , small  Ridge softer than jet – medium response  probably v 3 J. Putschke et al, QM06 Weak dependence of ridge yield on p T,trig  Relative contribution reduces with p T,trig 4 < p t,trig < 6 GeV/c Au+Au 0-10% STAR preliminary Jet-like peak p t,assoc. > 2 GeV/c

27. 27 0-12% 4.0 < p T trig < 6.0 GeV/c 6.0 < p T trig < 10.0 GeV/c 3.0 < p T trig < 4.0 GeV/c Preliminary Au+Au 0-12% 1.3 < p T assoc < 1.8 GeV/c Low p T trig : broad shape, two peaks High p T trig : broad shape, single peak Away-side shapes Fragmentation becomes ‘cleaner’ as p T trig goes up Suggests kinematic effect? M. Horner, M. van Leeuwen, et al

28. 28 v 3, triangular flow Alver and Roland, PRC81, 054905 Participant fluctuations lead to triangular component of initial state anisotropy This may well be the underlying mechanism for both ‘ridge’ and ‘Mach cone’

29. 29 Jet reconstruction Single, di-hadrons: focus on a few fragments of the shower  No information about initial parton energy in each event Jet finding: sum up fragments in a ‘jet cone’ Main idea: recover radiated energy – determine energy of initial parton Feasibility depends on background fluctuations, angular broadening of jets Need: tracking or Hadron Calorimeter and EMCal (  0 )

30. 30 Generic expectations from energy loss Longitudinal modification: –out-of-cone  energy lost, suppression of yield, di-jet energy imbalance –in-cone  softening of fragmentation Transverse modification –out-of-cone  increase acoplanarity k T –in-cone  broadening of jet-profile kT~kT~ E jet fragmentation after energy loss?

31. 31 Modified fragmentation functions A. Majumder, MvL, arXiv:1002.2206 z = p h|| /E jet Fragmentation function ratio  =ln(E Jet /p hadron ) z Borghini and Wiedemann Fragmentation function ‘Hump-backed plateau’ Expect softening of fragmentations: fewer fragments at high p T, more at low p T

32. 32 Jet shapes Energy distribution in sub-jets Energy loss changes radial distribution of energy Several ‘new’ observables considered Discussion: sensitivity  viability … ongoing q-Pythia, Eur Phys J C 63, 679

33. 33 Fixing the parton energy with  -jet events T. Renk, PRC74, 034906  -jet: know jet energy  sensitive to P(  E) R AA insensitive to P(  E) Nuclear modification factor Away-side spectra in  -jet E  = 15 GeV Away-side spectra for  -jet are sensitive to P(  E)  Input energy loss distribution

34. 34 I AA (z T ) = D AA (z T ) D pp (z T ) Direct-  recoil suppression Large suppression for away-side: factor 3-5 Reasonable agreement with model predictions  8 < E T,  < 16 GeVSTAR, arXiv:0912.1871 NB: gamma p T = jet p T still not very large

35. 35 Thermal photons PHENIX, PRL 104, 132301 Idea: hot quark-gluon matter radiates photons which escape Difficult measurement: Large background  0 →  Thermal photons at low p T Excess of photons seen at RHIC

36. 36 Jet reconstruction algorithms Two categories of jet algorithms: Sequential recombination k T, anti-k T, Durham –Define distance measure, e.g. d ij = min(p Ti,p Tj )*R ij –Cluster closest Cone –Draw Cone radius R around starting point –Iterate until stable ,  jet = particles For a complete discussion, see: http://www.lpthe.jussieu.fr/~salam/teaching/PhD-courses.html Sum particles inside jet Different prescriptions exist, most natural: E-scheme, sum 4-vectors Jet is an object defined by jet algorithm If parameters are right, may approximate parton

37. 37 Collinear and infrared safety Illustration by G. Salam Jets should not be sensitive to soft effects (hadronisation and E-loss) -Collinear safe -Infrared safe

38. 38 Jet finding in heavy ion events  η p t per grid cell [GeV] STAR preliminary ~ 21 GeV FastJet:Cacciari, Salam and Soyez; arXiv: 0802.1188 http://rhig.physics.yale.edu/~putschke/Ahijf/A_Heavy_Ion_Jet-Finder.html Jets clearly visible in heavy ion events at RHIC Use different algorithms to estimate systematic uncertainties: Cone-type algorithms simple cone, iterative cone, infrared safe SISCone Sequential recombination algorithms k T, Cambridge, inverse k T Combinatorial background Needs to be subtracted

39. 39 Jet finding with background By definition: all particles end up in a jet With background: all  -  space filled with jets Many of these jets are ‘background jets’

40. 40 Background subtraction STAR Preliminary multiplicity Background energy density (GeV) Background density at RHIC: 60-100 GeV Strong dependence on centrality Fluctuations remain after subtraction: RMS up to 10 GeV

41. 41 Jets at LHC LHC: jet energies up to ~200 GeV in Pb+Pb from 1 ‘short’ run Large energy asymmetry observed for central events

42. 42 Jets at LHC Centrality ATLAS, arXiv:1011.6182 (PRL) Jet-energy asymmetry Large asymmetry seen for central events N.B. only measures reconstructed di-jets Does not show ‘lost’ jets Large effect on recoil: qualitatively consistent with RHIC jet I AA Energy losses: tens of GeV, ~ expected from BDMPS, GLV etc beyond kinematic reach at RHIC

43. 43 Jets at LHC CMS, arXiv:1102.1957 CMS sees similar asymmetries

44. 44 Summary Hard processes can be used to probe quark-gluon matter So far: main focus on energy loss of (leading) high-p T hadrons –Integrates over initial energy, energy-loss For radiative energy loss expect  E  L 2 –Di-hadron recoil suppression confirms this –Azimuthal dependence of energy loss (v 2 at high p T ) not yet quantitatively understood Future directions: better handle on initial parton energy –Jet finding –  -jet

45. 45 Extra slides

46. 46 Hard probes of QCD matter Use the strength of pQCD to explore QCD matter Hard-scatterings produce ‘quasi-free’ partons  Initial-state production known from pQCD  Probe medium through energy loss Heavy-ion collisions produce ‘quasi-thermal’ QCD matter Dominated by soft partons p ~ T ~ 100-300 MeV Sensitive to medium density, transport properties

47. 47 Toy model R AA This is a cartoon! Hadronic, not partonic energy loss No quark-gluon difference Energy loss not probabilistic P(  E) Ball-park numbers:  E/E ≈ 0.2, or  E ≈ 2 GeV for central collisions at RHIC  0 spectra Nuclear modification factor PHENIX, PRD 76, 051106, arXiv:0801.4020 Note: slope of ‘input’ spectrum changes with p T : use experimental reach to exploit this

48. 48 Collinear safety Note also: detector effects, such as splitting clusters in calorimeter (  0 decay) Illustration by G. Salam

49. 49 Infrared safety Infrared safety also implies robustness against soft background in heavy ion collisions Illustration by G. Salam

50. 50 Shockwave/Mach Cone Gyulassy et al arXiv:0807.2235 T. Renk, J. Ruppert B. Betz, QM09, PRC79, 034902 Mach-cone/shockwave in the QGP? Exciting possibility! Are more mundane possibilities ruled out? – Not clear yet Proves that QGP is really ‘bulk matter’ Measure speed of sound?

51. 51 Jet broadening II Diffuse broadening Hard radiation/splitting Qualitatively, two different possible scenarios Different measurements: -R(0.2/0.4) -Transverse jet profile May have different sensitivities Interesting idea: sub-jet structure; so far no studies available Radiated energy ‘uniformly’ distributed Radiated energy directional

52. 52 Determining the medium density PQM (Loizides, Dainese, Paic), Multiple soft-scattering approx (Armesto, Salgado, Wiedemann) Realistic geometry GLV (Gyulassy, Levai, Vitev), Opacity expansion (L/ ), Average path length WHDG (Wicks, Horowitz, Djordjevic, Gyulassy) GLV + realistic geometry ZOWW (Zhang, Owens, Wang, Wang) Medium-enhanced power corrections (higher twist) Hard sphere geometry AMY (Arnold, Moore, Yaffe) Finite temperature effective field theory (Hard Thermal Loops) For each model: 1.Vary parameter and predict R AA 2.Minimize  2 wrt data Models have different but ~equivalent parameters: Transport coeff. Gluon density dN g /dy Typical energy loss per L:  0 Coupling constant  S PHENIX, arXiv:0801.1665, J. Nagle WWND08

53. 53 Medium density from R AA PQM = 13.2 GeV 2 /fm +2.1 - 3.2 ^ GLV dN g /dy = 1400 +270 - 150 WHDG dN g /dy = 1400 +200 - 375 ZOWW  0 = 1.9 GeV/fm +0.2 - 0.5 AMY  s = 0.280 +0.016 - 0.012 Data constrain model parameters to 10-20% Method extracts medium density given the model/calculation Theory uncertainties need to be further evaluated e.g. comparing different formalisms, varying geometry But models use different medium parameters – How to compare the results?

54. 54 Some pocket formula results Large differences between models GLV/WHDG: dN g /dy = 1400 T(  0 ) = 366 MeV PQM: (parton average) T = 1016 MeV AMY: T fixed by hydro (~400 MeV),  s = 0.297 – After long discussions, it turns out that most of these differences are mostly due to uncontrolled approximations in the calculations  Best guess: the truth is somewhere in-between

55. 55 Comparing single- and di-hadron results Armesto, Cacciari, Salgado et al. R AA and I AA fit with similar density Calculation uses LPM-effect, L 2 dependence

56. 56 QCD : For SU(3) : N c = 3 C A = 3, C F = 4/3 C F ~ strength of a gluon coupling to a quark C A ~ strength of the gluon self coupling T F ~ strength of gluon splitting into a quark pair C A /C F =9/4 Color factors Color factors measured at LEP Expect gluons radiate ~ twice more energy than quarks

57. 57 PYTHIA (by Adam Kocoloski) gg qq gq Subprocesses and quark vs gluon p+pbar dominantly from gluon fragmentation

58. 58 PRL 97, 152301 (2006) STAR Preliminary, QM08 Curves: X-N. Wang et al PRC70(2004) 031901 Baryon & meson NMF STAR Preliminary Comparing quark and gluon suppression Protons less suppressed than pions, not more No sign of large gluon energy loss

59. 59 Quark vs gluon suppression + renk plot WHDG Renk and Eskola, PRC76,027901 GLV formalism BDMPS formalism Quark/gluon difference larger in GLV than BDMPS (because of cut-off effects  E < E jet ?) ~10% baryons from quarks, so baryon/meson effect smaller than gluon/quark Are baryon fragmentation functions under control? Conclusion for now: some homework to do...

60. 60 The fine-print: background 3.0 < p T trig < 4.0 GeV/c 1.3 < p T assoc < 1.8 GeV/c High p T : background <~ signal 8 < p T trig < 15 GeV p T assoc > 3 GeV Low p T : background >> signal v 2 modulated background v 2trig * v 2assoc ~ few per cent Background normalisation: Zero Yield At Minimum N.B. no signal-free region at low p T

61. 61 v 3 in Hydro Schenke, Jeon, Gale, PRL 106, 042301 Evolution of initial state spatial anisotropy depends on viscosity

62. 62 v 3 vs eps v 3 from AMPT Schenke and Jeon v 3 from Hydrodynamics Alver and Roland Initial triangular anysotropy gives rise to v 3 in both parton cascade and hydrodynamics v 3 can be the underlying mechanism for both ‘ridge’ and ‘Mach cone’

63. 63 Modelling azimuthal dependence A. Majumder, PRC75, 021901 R AA p T (GeV) R AA R AA vs reaction plane sensitive to geometry model

64. 64 pQCD illustrated CDF, PRD75, 092006 jet spectrum ~ parton spectrum fragmentation

65. 65 R AA vs reaction plane angle Azimuthal modulation, path length dependence largest in ASW-BDMPS Data prefer ASW-BDMPS But why? – No clear answer yet Majumder, van Leeuwen, arXiv:1002.2206

66. 66 Interpreting di-hadron measurements Scenario I: Some lose all, Some lose nothing Scenario II: All lose something Di-hadron measurement: Away-side yield is (semi-)inclusive, so does not measure fluctuations of energy loss Multi-hadron measurements potentially more sensitive All is encoded in energy loss distribution P(  E)

67. 67 A closer look at azimuthal peak shapes No away-side broadening: -No induced radiation -No acoplanrity (‘multiple-scattering’)   Induced acoplanarity (BDMPS): Vitev, hep-ph/0501225 Broadening due to fragments of induced radiation 8 < p T (trig) < 15 GeV/c p T (assoc)>6 GeV

68. 68 Fragmentation functions Qualitatively: Fragmentation functions sensitive to P(  E) Distinguish GLV from BDMPS?

69. 69 Parton energy loss and R AA modeling Qualitatively: `known’ from e + e - known pQCDxPDF extract Parton spectrum Fragmentation (function) Energy loss distribution medium effect Medium effect P(  E) is only part of the story Parton spectrum and fragmentation function are steep  non-trivial relation between R AA and P(  E)